Problem: What's the first wrong statement in the proof below that $ \triangle EBC \cong \triangle EBD$ $ \; ?$ $ \overline{BC} $ is parallel to $ \overline{DF} $. This diagram is not drawn to scale. $A$ $B$ $C$ $D$ $E$ $F$ Givens $ \angle DBE \cong \angle CFE$ $, \ $ $ \overline{BE} \cong \overline{EF}$ $, \ $ $ \angle BED \cong \angle CEF$ $, \ $ $ \angle DBE \cong \angle ABC$ $, \ $ $ \overline{BE} \cong \overline{AB}$ $, \ $ and $\ $ $ \angle BED \cong \angle BAC$ Proof $ \triangle EFC \cong \triangle EBD$ because ASA $ \overline{CE} \cong \overline{DE}$ because corresponding parts of congruent triangles are congruent $ \overline{AC} \cong \overline{AF}$ because corresponding parts of congruent triangles are congruent $ \angle BDE \cong \angle ECF$ because corresponding parts of congruent triangles are congruent $ \triangle ABC \cong \triangle EBD$ because ASA $ \triangle EBC \cong \triangle EBD$ because SSS
Solution: Try going through the proof yourself: write down the givens, and then see if they justify the next step for the reason given. Then do the same thing for the next step, and the next, until you run into something that you can't justify, or you finish the proof. $ \overline{AF} \cong \overline{AC}$ is the first wrong statement.